Exam 5: Several Useful Discrete Distributions

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, what is P(x = 0)?

Suppose 40% of the TV sets in use in Canada on a particular night were tuned into game 7 of the Stanley Cup Playoffs. a. If we were to take a sample of six in-use TV sets that night, what is the probability exactly three are tuned to the Stanley Cup Playoffs? b. If, instead, the sample consisted of 15 in-use TVs, what is the probability 5 or more are tuned to the Stanley Cup Playoffs?

The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is known that 70% of Canadians are "tasters" and 30% are "non-tasters." Suppose a genetics class of size 20 does the test to see if they match the Canadian percentage of "tasters" and "non-tasters." (Assume the assignment of students to classes constitutes a random process.) a. What is the probability distribution of the random variable x, the number of "non-tasters" in the class? b. Find P(3 < x < 9). c. Find the mean of x. d. Find the variance of x.

The mean and variance of a Poisson distribution variable are equal.

Job Applicants Narrative A company has five applicants, three women and two men, for two positions. Suppose that the five applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of men chosen to fill the two positions. -Refer to Job Applicants Narrative. Write the formula for p(x), the probability distribution of x.

A package of six light bulbs contains two defective bulbs. If three bulbs are selected for use, find the probability none are defective.